In this paper, we investigate two different constant-coefficient nonlinear evolution equations, namely the Schamel Burgers equation and the Schamel equation. These models also have a great deal of potential for studying ion-acoustic waves in plasma physics and fluid dynamics. The primary goal of this paper is to establish closed-form solutions and dynamics of analytical solutions to the Schamel Burgers and the Schamel equations, which are special examples of the well-known Schamel–Korteweg-de Vries (S-KdV) equation. We derive completely novel solutions to the considered models using a variety of computation programmes and a newly proposed extended generalized (G′ G ) expansion approach. The newly formed solutions, which include hyperbolic and trigonometric functions as well as rational function solutions, have been produced. The annihilation of three-dimensional shock waves, periodic waves, single soliton, singular soliton, and combo soliton, multisoliton as well as their three-dimensional and contour plots are used to show the dynamical representations of the acquired solutions. These results demonstrate that the proposed extended technique is efficient, reliable and simple.

中文翻译：

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使用新的分析方法对具有恒定系数的 Schamel Burgers 和 Schamel 方程的精确闭式解的动力学

在本文中，我们研究了两个不同的常数系数非线性演化方程，即Schamel Burgers 方程和Schamel 方程。这些模型在研究等离子体物理学和流体动力学中的离子声波方面也具有很大的潜力。本文的主要目标是建立 Schamel Burgers 和 Schamel 方程的解析解的封闭形式解和动力学，它们是著名的 Schamel-Korteweg-de Vries (S-KdV) 方程的特殊示例。我们使用各种计算程序和新提出的扩展广义(G' G )扩展方法。新形成的解，包括双曲和三角函数以及有理函数解，已经产生。三维冲击波、周期波、单孤子、奇异孤子、组合孤子、多孤子的湮灭以及它们的三维和等高线图用于显示所获得解的动力学表示。这些结果表明，所提出的扩展技术是高效、可靠和简单的。